############################################################################## ## ## Green functions for ## F_4(q), q power of good prime ## ## http://www.math.rwth-aachen.de/~Frank.Luebeck/chev/Green/ ## Frank.Luebeck@Math.RWTH-Aachen.de ## ## This file can be read with GAP 3 or GAP 4. # defining q if not bound and a helper function if not IsBound(SetName) then FamilyObj:=0;LaurentPolynomialByCoefficients:=0; fi; if not IsBound(q) then q := Indeterminate(Cyclotomics); if not IsBound(SetName) then q.name := "q"; else SetName(q,"q"); fi; fi; if q = Indeterminate(Cyclotomics) then if not IsBound(SetName) then tmpf:=function(cv) return Polynomial(Cyclotomics,cv[1],cv[2]);end; else tmpf := function(cv) return LaurentPolynomialByCoefficients( FamilyObj(1),cv[1],cv[2]); end; fi; else if not IsBound(SetName) then tmpf:=function(cv) return Value(Polynomial(Cyclotomics,cv[1],cv[2]),q);end; else tmpf := function(cv) return Value(LaurentPolynomialByCoefficients( FamilyObj(1),cv[1],cv[2]),q); end; fi; fi; tmpff := function(t) t.GFOrder := tmpf(t.GFOrder); t.classLengths := List(t.classLengths,tmpf); t.table := List(t.table,r-> List(r,tmpf)); end; greenF4good := rec( classLengths := [ [ [ 1 ], 0 ], [ [ -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 ], 0 ], [ [ -1/2, 0, 0, -1/2, -1/2, 0, 0, -1/2, 0, 0, 0, 0, 1/2, 0, 0, 1/2, 1/2, 0, 0, 1/2 ], 3 ], [ [ 1/2, 0, 0, -1/2, 1/2, 0, 0, -1/2, 0, 0, 0, 0, -1/2, 0, 0, 1/2, -1/2, 0, 0, 1/2 ], 3 ], [ [ 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -2, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1 ], 4 ], [ [ 1/2, 0, 0, 1/2, 0, 0, 0, 0, -1/2, 0, 0, -1/2, -1/2, 0, 0, -1/2, 0, 0, 0, 0, 1/2, 0, 0, 1/2 ], 7 ], [ [ -1/2, 0, 0, 1/2, 0, 0, 0, 0, 1/2, 0, 0, -1/2, 1/2, 0, 0, -1/2, 0, 0, 0, 0, -1/2, 0, 0, 1/2 ], 7 ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1 ], 10 ], [ [ -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1 ], 8 ], [ [ -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 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], [ [ -1 ], 6 ], [ [ ], 0 ], [ [ ], 0 ], [ [ ], 0 ], [ [ ], 0 ], [ [ ], 0 ], [ [ ], 0 ], [ [ ], 0 ] ] ], name := "Green( F_4(q) ), 1 mod 6", classInfo := [ [ "A_0", 1 ], [ "A_1", 1 ], [ "~A_1", 1 ], [ "~A_1", 2 ], [ "A_1 + ~A_1", 1 ], [ "A_2", 1 ], [ "A_2", 2 ], [ "~A_2", 1 ], [ "A_2 + ~A_1", 1 ], [ "~A_2 + A_1", 1 ], [ "B_2", 1 ], [ "B_2", 2 ], [ "C_3(a_1)", 1 ], [ "C_3(a_1)", 2 ], [ "F_4(a_3)", 1 ], [ "F_4(a_3)", 2 ], [ "F_4(a_3)", 3 ], [ "F_4(a_3)", 4 ], [ "F_4(a_3)", 5 ], [ "C_3", 1 ], [ "B_3", 1 ], [ "F_4(a_2)", 1 ], [ "F_4(a_2)", 2 ], [ "F_4(a_1)", 1 ], [ "F_4(a_1)", 2 ], [ "F_4", 1 ] ], charInfo := [ [ "L=A_0", "A_0" ], [ "L=A_0", "4A_1" ], [ "L=A_0", "2A_1" ], [ "L=A_0", "A_2" ], [ "L=A_0", "D_4" ], [ "L=A_0", "D_4(a_1)" ], [ "L=A_0", "~A_2" ], [ "L=A_0", "C_3 + A_1" ], [ "L=A_0", "A_2 + ~A_2" ], [ "L=A_0", "F_4(a_1)" ], [ "L=A_0", "F_4" ], [ "L=A_0", "A_1" ], [ "L=A_0", "3A_1" ], [ "L=A_0", "~A_2 + A_1" ], [ "L=A_0", "C_3" ], [ "L=A_0", "A_3" ], [ "L=A_0", "~A_1" ], [ "L=A_0", "2A_1 + ~A_1" ], [ "L=A_0", "A_2 + ~A_1" ], [ "L=A_0", "B_3" ], [ "L=A_0", "B_2 + A_1" ], [ "L=A_0", "A_1 + ~A_1" ], [ "L=A_0", "B_2" ], [ "L=A_0", "A_3 + ~A_1" ], [ "L=A_0", "B_4" ], [ "L=F_4", [ 1 ] ] ], GFOrder := [ [ 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0, 2, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1 ], 24 ] ); tmpff(greenF4good); Unbind(tmpvari); Unbind(tmpvarj);Unbind(tmpf);Unbind(tmpff);